Coding language in C

1st program:

2nd program:

3rd program:

The values of the Combinations function used in the text are often displayed in the form of a triangle using the following arrangement: C(0,0) C(1,0) C(1,1) C(2,0) C(2,1) C(2,2) C(3,0) C(3,1) C(3,2) C(3,3) C(4,0) C(4,1) C(4,2) C(4,3) C(4,4) and so on. this figure is called Pascal's Triangle after the seventeenth-century French mathematician Blaise Pascal, who invented it. Pascal's Triangle has the interesting property that every interior entry is the sum of the two entries above it. Write a C program to display the first eight rows of Pascal's Triangle like this: 1 2 1 1 3 3 1 4 6 4 1 5 10 1 1 1 6 7 15 20 10 15 35 5 6 21 1 1 21 35 7 1 To figure out the spacing for each line, think about how many characters each line occupies. Then analyze how that character number relates to the row number. In many cases, it is not enough to know whether a number is prime; sometimes, you need to know its factors. Every positive integer greater than 1 can be expressed as a product of prime numbers. This factorization is unique and is called the prime factorization. For example, the number 60 can be decomposed into the factors 2 x 2 x 3 x 5, each of which is prime. Note that the same prime can appear more than once in the factorization. Write a program to display the prime factorization of a number n. The following is a sample run of the program: Enter number to be factored: 60 - 2 * 2 * 3 * 5 the library might be useful. Also, you might need to define TRUE and FALSE to be 1 and 0, respectively. The technique of series approximation can be used to compute approximations of the mathematical constant a. One of the simplest series that involves a is the following: 1 1 1 1 1 I--+- -- +--- t... 3.5 7 9 11 A Write a program that calculates an approximation of a consisting of the first 10,000 terms in the series above. Use %12.101f to print the value of pi